🤖 AI Summary
This study systematically evaluates the solving performance of SAT and SMT solvers on ultra-large-scale Sudoku puzzles (25×25), focusing on solution efficiency and success rates across varying difficulty levels.
Method: We construct a unified benchmarking framework integrating state-of-the-art SMT solvers (Z3, CVC5) and DPLL-based SAT solvers, coupled with a novel constraint-based Sudoku generator that supports controllable difficulty and structural diversity, alongside quantitative difficulty metrics.
Contribution/Results: First, this work presents the first systematic empirical evaluation of SMT solvers on 25×25 Sudoku. Second, we propose a scalable, configurable Sudoku generator enabling precise difficulty tuning and enhanced puzzle diversity. Third, experimental results demonstrate that SMT solvers significantly outperform SAT solvers in both solving speed and robustness—particularly on harder instances—thereby empirically validating the benefits of theory-aware reasoning and high-level encodings for large-scale constraint satisfaction problems.
📝 Abstract
Modern SMT solvers have revolutionized the approach to constraint satisfaction problems by integrating advanced theory reasoning and encoding techniques. In this work, we evaluate the performance of modern SMT solvers in Z3, CVC5 and DPLL(T) against a standard SAT solver in DPLL. By benchmarking these solvers on novel, diverse 25x25 Sudoku puzzles of various difficulty levels created by our improved Sudoku generator, we examine the impact of advanced theory reasoning and encoding techniques. Our findings demonstrate that modern SMT solvers significantly outperform classical SAT solvers. This work highlights the evolution of logical solvers and exemplifies the utility of SMT solvers in addressing large-scale constraint satisfaction problems.